A Course of Mathematics for Engineers and Scientists. Volume by Brian H. Chirgwin PDF

By Brian H. Chirgwin

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Extra resources for A Course of Mathematics for Engineers and Scientists. Volume 3: Theoretical Mechanics

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60 = —6(p. , 2 T = W/1/3. Note that the tension in this special case has been calculated after writing down the equation of virtual work for the system under consideration in the general case. We do not insert the values of 0 and 97 corresponding to the specified configuration until the equation of virtual work (3) and the first order variation (1) of the equation of constraint have been written down. (iii) A frame is constructed of 5 heavy uniform bars which are smoothly jointed to form a regular pentagon ABCDE.

The coefficient of 60 gives 10 sin(0 y) — 7 sin(y — 0) + 4 sin(0 ± 2y — 99) -= 0. Since 99 =- v = nI4, 10 7 4 (sine + cos 0) — w(cos 0 — sin 9) + w(sin 0 + cos e) = 0 . •. 0 1 --y , , verifying that the line APF is vertical. The coefficient of (599 gives 4/11cos y = W {10 sin (0 + 92) + 7 sin (99 — 0) — 4 sin (0 + 2v — 99)). •. Tl = W V10. From the coefficient of Sip we obtain 4 T2 siny, = 8 W sin(0 21,v — 99) whence 772— yio w \ 5) Exercises 2:4 1. A uniform rod AB of weight W and length 2/ has one end A in contact with a smooth horizontal plane and it rests against a small smooth peg C at a distance n l from the plane (n < 2).

Three equal uniform rods AB, BC, CD, each of weight W, are smoothly jointed to one another at B and C and to two fixed points A, D in the same horizontal line. A light inextensible string joining B to D maintains ABCD in the shape of a rhombus with < BCD = 60°. Prove that when a weight 4 W is suspended from B the tension in the string is 2 1/3 W. 4. Six rods are freely jointed at their ends to form a hexagon ABCDEF with AB = CD = DE = FA = 2a each of weight W, , and BC = EF = 2 b each of weight W2 .

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A Course of Mathematics for Engineers and Scientists. Volume 3: Theoretical Mechanics by Brian H. Chirgwin


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